For a given input value $b$, the function $f$ outputs a value $a$ to satisfy the following equation. $4a + 7b = -52$ Write a formula for $f(b)$ in terms of $b$. $f(b)=$
Solution: $f(b)$ expresses $a$ as a function of $b$. To arrive at a correct formula, all we have to do is solve the equation for $a$. $ \begin{aligned}4a+7b&=-52\\\\ 4a&=-52-7b\\\\ a&=\dfrac{-52}{4}-\dfrac{7b}{4}\\\\ a&=-13-\dfrac{7}{4}b\end{aligned}$ Therefore, this formula expresses $a$ as a function of $b$ : $ f(b)=-13-\dfrac{7}{4}b$